Bipartitle eQTL Network Construction
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evaluate eQTL by modeling the association between SNP genotypes and gene expression.
- an r×n matrix S of SNP genotypes
- r×m matrix G of gene expression
each with r rows representing observations and columns representing n SNPs and m genes, respectively
consider a covariate matrix X, including features such as principal components for population structure, sex and age.
model the eQTL of a particular SNP i on a locus’s gene expression j
Gj=X⊤α+βijSithe eQTL association between all pairs of SNPs and genes can be represented as a bipartitle network by considering each SNP i and gene j to be a node in the network, and casting a function of their association as edges
define a set of adjacency matrix representations based on summary statistics from eQTL analyses
aij=|zij|I{Yij<τ},where
- zij is either set equal to 1 for an unweighted representation or the z-statistic for testing βij from the eQTL regression between SNP i and gene j for a weighted representation
- Yij is a measure of the significance of the eQTL association
three definitions of Y
to identify nodes (either SNPs or genes in the bipartite representation) that are central to the network
consider the network metric of degree
for the sparse representation of A, the degree of SNP i and the degree of gene j are defined as follows